I copied and read your COMPUTER MODELS OF SELECTION, EVOLUTION, AND PUNC-EQ
from your website. I am impressed with it. I'll go along with your formulas
and results since I do not have the training to do anything else. I agree
that your figures are beautiful. I regret I could not print them in color.
But I did print them in black and white and they turned out quite well. I
estimate I used up about 5 bucks worth of toner doing so.
I have some questions and comments. First about the selection program you
used. You said on p. 1, "Selection is a program which mimics the process of
natural selection. When the program starts, one can select the type of
geometric form you want to select for." Here's the problem as I see it.
Your selection program does not really mimic the process of natural
Natural selection does not look ahead to some distant goal or target (which
in your program is a chosen geometric form). Natural selection, a la Darwin,
operates on the criterion of immediate survivability, adaptation, and/or
increased reproductive success. If the phenotype has an edge over others in
survivability, etc., it is selected by the environment. Darwin wrote,
"individuals having any advantage, however, slight, over others, would have
the best chance of surviving and of procreating their kind. Only those
variations which are in some way profitable will be preserved or naturally
selected" (p. 81, 119, Everyman's Library edition).
What you have used, in my opinion, is the process of *artificial selection*,
or investigator intervention, as Thaxton, et. al. call it. Darwin also used
artificial selection of pigeons and dogs as his analogy of natural selection.
The target was some ideal distant target-form that the breeder chose.
Dawkins, used the human eye as his selecting agent in his computer
simulations of natural selection. He said, "The human eye has an active role
to play in the story. It is the selecting agent. It surveys the litter of
progeny and chooses the one for breeding" (Blind Watchmaker, p. 57). By
employing an external intelligent being to provide a distant target all three
of you have missed the heart of natural selection, which is that selection
has no distant guide, it operates only for *immediate* survival and
Then you went on to run a program with no selection at all. On p. 3 you
said, "There is one final option and that is to have no selection at all."
I am puzzled by this option. What has it to do with natural selection?
Underlying your computer programs is what I perceive to be a willingness on
your part to accept almost any change or pattern generation as an example or
analogy of natural selection. I agree with Thomson, "Scientists can always
do themselves a great service by being scrupulously precise about the nature
of their statements" (Amer. Sci., Sep.-Oct, 1982). Natural selection is a
very precise term. As I see it you are using it so loosely that almost
Secondly, I appreciate the comment you made on the third page, where you
wrote, "One final thing. I do not want this to be taken as an attack on the
Bible. I believe that God Created the world, and the design of mathematical
systems such as these nonlinear systems are evidence of that. Belief in
evolution does not preclude belief in the God of the Bible."
I for one have never questioned your commitment to the God of the Bible. But
here is my comment: I do not see you actively trying to *integrate* your
belief in God with your scientific pursuit of evolutionary theory. I see you
running your computer simulations, with no mention of God, and then assuring
us later that you are committed to the God of the Bible. To be sure, God
created the nonlinear systems, as you say, and all the other initial
conditions and laws of the universe. Don't deists believe the same? I
think we need to go beyond that. For instances, do you think God enters into
the process of natural selection and if so, where and how? Does God see to
it that certain desired mutations occur? Does God roll the dice? Is God the
Selective Agent, working through the environment to see that certain desired
Those are my questions and comments on your paper, Glenn, which I repeat is a
interesting and impressive piece of work.